A geometric multigrid solver for the free-surface equation in environmental models featuring irregular coastlines

Pieter Rauwoens, Peter A Troch, Jan Vierendeels

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Abstract A recently developed multigrid method (Botto, 2013), based on the concept of volume fraction, has been tested for the inversion of the Helmholz-type equation for the free surface in the environmental public domain code COHERENS. The volume fraction concept is particularly interesting for coarse grid cells that are agglomerated from both dry and wet fine grid cells at irregular coastlines. At these locations, modifying the prolongation operator and the coarse grid discretization, using the volume fraction, results in better convergence. However, as convergence deteriorates in the case of small, elongated islands that tend to disappear by the multigrid coarsening procedure, a correction is proposed, yielding good convergence rates, irrespective of the presence of small or large islands. The method is tested extensively for the inversion of the academic Poisson equation. Larger test cases, solving the Helmholz-type equation, prove the applicability for real-life applications of environmental flows.

Original languageEnglish (US)
Article number10084
Pages (from-to)22-36
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume289
DOIs
StatePublished - Jun 3 2015
Externally publishedYes

Fingerprint

Volume Fraction
Free Surface
Irregular
Volume fraction
Grid
Inversion
A.s. Convergence
Prolongation
Cell
Poisson equation
Multigrid Method
Coarsening
Poisson's equation
Rate of Convergence
Discretization
Model
Tend
Operator
Concepts

Keywords

  • Helmholz equation
  • Multigrid
  • Poisson equation
  • Shallow water flow
  • Small island problem
  • Stair-case boundary

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

A geometric multigrid solver for the free-surface equation in environmental models featuring irregular coastlines. / Rauwoens, Pieter; Troch, Peter A; Vierendeels, Jan.

In: Journal of Computational and Applied Mathematics, Vol. 289, 10084, 03.06.2015, p. 22-36.

Research output: Contribution to journalArticle

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N2 - Abstract A recently developed multigrid method (Botto, 2013), based on the concept of volume fraction, has been tested for the inversion of the Helmholz-type equation for the free surface in the environmental public domain code COHERENS. The volume fraction concept is particularly interesting for coarse grid cells that are agglomerated from both dry and wet fine grid cells at irregular coastlines. At these locations, modifying the prolongation operator and the coarse grid discretization, using the volume fraction, results in better convergence. However, as convergence deteriorates in the case of small, elongated islands that tend to disappear by the multigrid coarsening procedure, a correction is proposed, yielding good convergence rates, irrespective of the presence of small or large islands. The method is tested extensively for the inversion of the academic Poisson equation. Larger test cases, solving the Helmholz-type equation, prove the applicability for real-life applications of environmental flows.

AB - Abstract A recently developed multigrid method (Botto, 2013), based on the concept of volume fraction, has been tested for the inversion of the Helmholz-type equation for the free surface in the environmental public domain code COHERENS. The volume fraction concept is particularly interesting for coarse grid cells that are agglomerated from both dry and wet fine grid cells at irregular coastlines. At these locations, modifying the prolongation operator and the coarse grid discretization, using the volume fraction, results in better convergence. However, as convergence deteriorates in the case of small, elongated islands that tend to disappear by the multigrid coarsening procedure, a correction is proposed, yielding good convergence rates, irrespective of the presence of small or large islands. The method is tested extensively for the inversion of the academic Poisson equation. Larger test cases, solving the Helmholz-type equation, prove the applicability for real-life applications of environmental flows.

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